An object of mass 1.15 kg is attached to a horizontal spring and set sliding bac

Question

An object of mass 1.15 kg is attached to a horizontal spring and set sliding back and forth on a frictionless surface, oscillating between the points x1 = -0.158 m and x2 = 0.158 m. While it oscillates, you measure that it takes 129 s for the object to complete 81 full back-and-forth oscillations. What is the kinetic energy of the mass and spring when the mass is at the point x1 = -0.158 m? What is the kinetic energy of the mass and spring when the mass is at the midpoint between x1 = -0.158 m and x2 = 0.158 m?

Explanation / Answer

at extreme point, mass will be at rest.

so KE at x = - 0.158 m , KE = 0 ..........Ans

When at midpoint,

T = 129 / 81 = 1.59 sec ....Time period

w = 2pi / T = 3.94 rad/s

v_max = A w = 0.158 x 3.94 = 0.623 m/s

KE = m v_max^2 / 2

= 1.15 x 0.623^2 /2

= 0.223 J .......Ans

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